Dictionary

adjunction en · NOUN

Pronunciation

• (US) audio

Etymology

From Latin adjunctio, from adjungere: compare French adjonction, and see adjunct.

Meanings

1. (countable, uncountable) The act of joining; the thing joined or added.
2. (countable, uncountable) The joining of personal property owned by one to that owned by another.
3. (countable, uncountable) The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.
   • The ring obtained after the adjunction of the elements a,b and y to the ring R may be denoted R#91;a,b,y#93;.
   • The field adjunction #92;mathbb#123;Q#125;(#92;pi) can be obtained from #92;mathbb#123;Q#125; by adjoining #92;pi to #92;mathbb#123;Q#125;.
4. (broadly, countable, uncountable) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
5. (countable, qualifier:strictly, uncountable) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.
6. (countable, formal, qualifier:strictly, uncountable) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object. ▸ A natural isomorphism Φ: operatorname Hom_( mathcal )C(G·,·)→ operatorname Hom_( mathcal )D(·,F·) (where the hom-functors are understood as bifunctors from 𝒟^( operatorname )op×𝒞 to mathbf Set). See Adjoint functors on Wikipedia.Wikipedia .

Forms

Deriveds

biadjunction

Hyponyms

Galois connection · isomorphism of categories · equivalence of categories

Meronyms

right adjoint · adjoint · left adjoint

Translations (4)

pl adiunkcja (the act of joining) · fi liittäminen (the act of joining) · pt adjunção (the act of joining) · pl adiunkcja (a form of similarity between a pair of categories mapped to each other by dual morphisms)